Optogenetic perturbations reveal the dynamics of an oculomotor integrator

Many neural systems can store short-term information in persistently firing neurons. Such persistent activity is believed to be maintained by recurrent feedback among neurons. This hypothesis has been fleshed out in detail for the oculomotor integrator (OI) for which the so-called “line attractor” network model can explain a large set of observations. Here we show that there is a plethora of such models, distinguished by the relative strength of recurrent excitation and inhibition. In each model, the firing rates of the neurons relax toward the persistent activity states. The dynamics of relaxation can be quite different, however, and depend on the levels of recurrent excitation and inhibition. To identify the correct model, we directly measure these relaxation dynamics by performing optogenetic perturbations in the OI of zebrafish expressing halorhodopsin or channelrhodopsin. We show that instantaneous, inhibitory stimulations of the OI lead to persistent, centripetal eye position changes ipsilateral to the stimulation. Excitatory stimulations similarly cause centripetal eye position changes, yet only contralateral to the stimulation. These results show that the dynamics of the OI are organized around a central attractor state—the null position of the eyes—which stabilizes the system against random perturbations. Our results pose new constraints on the circuit connectivity of the system and provide new insights into the mechanisms underlying persistent activity

Derived equivalence classification of the cluster-tilted algebras of Dynkin type E

We obtain a complete derived equivalence classification of the cluster-tilted algebras of Dynkin type E. There are 67, 416, 1574 algebras in types E6, E7 and E8 which turn out to fall into 6, 14, 15 derived equivalence classes, respectively. This classification can be achieved computationally and we outline an algorithm which has been implemented to carry out this task. We also make the classification explicit by giving standard forms for each derived equivalence class as well as complete lists of the algebras contained in each class; as these lists are quite long they are provided as supplementary material to this paper. From a structural point of view the remarkable outcome of our classification is that two cluster-tilted algebras of Dynkin type E are derived equivalent if and only if their Cartan matrices represent equivalent bilinear forms over the integers which in turn happens if and only if the two algebras are connected by a sequence of "good" mutations. This is reminiscent of the derived equivalence classification of cluster-tilted algebras of Dynkin type A, but quite different from the situation in Dynkin type D where a far-reaching classification has been obtained using similar methods as in the present paper but some very subtle questions are still open.Comment: 19 pages. v4: completely rewritten version, to appear in Algebr. Represent. Theory. v3: Main theorem strengthened by including "good" mutations (cf. also arXiv:1001.4765). Minor editorial changes. v2: Third author added. Major revision. All questions left open in the earlier version by the first two authors are now settled in v2 and the derived equivalence classification is completed. arXiv admin note: some text overlap with arXiv:1012.466

Field theory of scaling lattice models. The Potts antiferromagnet

In contrast to what happens for ferromagnets, the lattice structure participates in a crucial way to determine existence and type of critical behaviour in antiferromagnetic systems. It is an interesting question to investigate how the memory of the lattice survives in the field theory describing a scaling antiferromagnet. We discuss this issue for the square lattice three-state Potts model, whose scaling limit as T->0 is argued to be described exactly by the sine-Gordon field theory at a specific value of the coupling. The solution of the scaling ferromagnetic case is recalled for comparison. The field theory describing the crossover from antiferromagnetic to ferromagnetic behaviour is also introduced.Comment: 11 pages, to appear in the proceedings of the NATO Advanced Research Workshop on Statistical Field Theories, Como 18-23 June 200

Overdiagnosis and overtreatment of breast cancer: Overdiagnosis in randomised controlled trials of breast cancer screening

Data from randomised controlled trials of mammographic screening can be used to determine the extent of any overdiagnosis, as soon as either a time equivalent to the lead-time has elapsed after the final screen, or the control arm has been offered screening. This paper reviews those randomised trials for which breast cancer incidence data are available. In recent trials in which the control group has not been offered screening, an excess incidence of breast cancer remains after many years of follow-up. In those trials in which the control arm has been offered screening, although there is a possible shift from invasive to in situ disease, there is no evidence of overdiagnosis as a result of incident screens

Firms' Main Market, Human Capital and Wages

Recent international trade literature emphasizes two features in characterizing the current patterns of trade: efficiency heterogeneity at the firm level and quality differentiation. This paper explores human capital and wage differences across firms in that context. We build a partial equilibrium model predicting that firms selling in more-remote markets employ higher human capital and pay higher wages to employees within each education group. The channel linking these variables is firms’ endogenous choice of quality. Predictions are tested using Spanish employer-employee matched data that classify firms according to four main destination markets: local, national, European Union, and rest of the World. Employees’ average education is increasing in the remoteness of firm’s main output market. Market–destination wage premia are large, increasing in the remoteness of the market, and increasing in individual education. These results suggest that increasing globalization may play a significant role in raising wage inequality within and across education groups

CMAP Scan MUNE (MScan) - A Novel Motor Unit Number Estimation (MUNE) Method

Like other methods for motor unit number estimation (MUNE), compound muscle action potential (CMAP) scan MUNE (MScan) is a non-invasive electrophysiologic method to estimate the number of functioning motor units in a muscle. MUNE is an important tool for the assessment of neuropathies and neuronopathies. Unlike most MUNE methods in use, MScan assesses all the motor units in a muscle, by fitting a model to a detailed stimulus-response curve, or CMAP scan. It thereby avoids the bias inherent in all MUNE methods based on extrapolating from a small sample of units. Like 'Bayesian MUNE,' MScan analysis works by fitting a model, made up of motor units with different amplitudes, thresholds, and threshold variabilities, but the fitting method is quite different, and completed within five minutes, rather than several hours. The MScan off-line analysis works in two stages: first, a preliminary model is generated based on the slope and variance of the points in the scan, and second, this model is then refined by adjusting all the parameters to improve the fit between the original scan and scans generated by the model. This new method has been tested for reproducibility and recording time on 22 amyotrophic lateral sclerosis (ALS) patients and 20 healthy controls, with each test repeated twice by two blinded physicians. MScan showed excellent intra- and inter-rater reproducibility with ICC values of >0.98 and a coefficient of variation averaging 12.3 ± 1.6%. There was no difference in the intra-rater reproducibility between the two observers. Average recording time was 6.27 ± 0.27 min. This protocol describes how to record a CMAP scan and how to use the MScan software to derive an estimate of the number and sizes of the functioning motor units. MScan is a fast, convenient, and reproducible method, which may be helpful in diagnoses and monitoring disease progression in neuromuscular disorders

Recursive representation of the torus 1-point conformal block

The recursive relation for the 1-point conformal block on a torus is derived and used to prove the identities between conformal blocks recently conjectured by R. Poghossian. As an illustration of the efficiency of the recurrence method the modular invariance of the 1-point Liouville correlation function is numerically analyzed.Comment: 14 pages, 1 eps figure, misprints corrected and a reference adde